Stitching IC Images

Image stitching software is used in many areas such as photogrammetry, biomedical imaging, and even amateur digital photography. However, these algorithms require relatively large image overlap, and for this reason they cannot be used to stitch the integrated circuit (IC) images, whose overlap is typically less than 60 pixels for a 4096 by 4096 pixel image. In this paper, we begin by using algorithmic graph theory to study optimal patterns for adding IC images one at a time to a grid. In the remaining sections we study ways of stitching all the images simultaneously using different optimisation approaches: least squares methods, simulated annealing, and nonlinear programming

Neural networks in geophysical applications

Neural networks are increasingly popular in geophysics. Because they are universal approximators, these tools can approximate any continuous function with an arbitrary precision. Hence, they may yield important contributions to finding solutions to a variety of geophysical applications. However, knowledge of many methods and techniques recently developed to increase the performance and to facilitate the use of neural networks does not seem to be widespread in the geophysical community. Therefore, the power of these tools has not yet been explored to their full extent. In this paper, techniques are described for faster training, better overall performance, i.e., generalization,and the automatic estimation of network size and architecture

Uncertainty modelling in power system state estimation

This thesis was submitted for the degree of Doctor of Philosophy and was awarded by Brunel University.As a special case of the static state estimation problem, the load-flow problem is studied in this thesis. It is demonstrated that the non-linear load-flow formulation may be solved by real-coded genetic algorithms. Due to its global optimisation ability, the proposed method can be useful for off-line studies where multiple solutions are suspected. This thesis presents two methods for estimating the uncertainty interval in power system state estimation due to uncertainty in the measurements. The proposed formulations are based on a parametric approach which takes in account the meter inaccuracies. A nonlinear and a linear formulation are proposed to estimate the tightest possible upper and lower bounds on the states. The uncertainty analysis, in power system state estimation, is also extended to other physical quantities such as the network parameters. The uncertainty is then assumed to be present in both measurements and network parameters. To find the tightest possible upper and lower bounds of any state variable, the problem is solved by a Sequential Quadratic Programming (SQP) technique. A new robust estimator based on the concept of uncertainty in the measurements is developed here. This estimator is known as Maximum Constraints Satisfaction (MCS). Robustness and performance of the proposed estimator is analysed via simulation of simple regression examples, D.C. and A.C. power system models.Embassy of Kuwai

Essays on mixture autoregressive models with applications to macroeconomics and finance

This dissertation complements a family of mixture autoregressive models based on Gaussian and Student's t distributions by filling the gaps in the previous literature with four self contained essays. This includes univariate models as well as reduced form and structural multivariate models. Empirical applications to macroeconomics and finance demonstrate their usefulness. I have also accompanied this dissertation with open source software, in the form of R packages uGMAR and gmvarkit, which provide a comprehensive set of tools for estimation and other numerical analysis of the models. The software is distributed through the Comprehensive R Archive Network. The first essay introduces a new mixture autoregressive model that combines linear Gaussian autoregressions and linear Student's t autoregressions as its mixture components. The model has attractive properties analogous to the Gaussian and Student's t mixture autoregressive models, but it is more flexible as it enables to model series which consist of both conditionally homoskedastic Gaussian regimes and conditionally heteroskedastic Student's t regimes. The usefulness of the model is demonstrated in an empirical application to the monthly U.S. interest rate spread between the 3-month Treasury bill rate and the effective federal funds rate. The second essay describes the R package uGMAR, which provides tools for estimating and analysing the Gaussian mixture autoregressive model, the Student's t mixture autoregressive model, and the Gaussian and Student's t mixture autoregressive model. The model parameters are estimated with the method of maximum likelihood by running multiple rounds of a two-phase estimation procedure in which a genetic algorithm is used to find starting values for a gradient based method. For evaluating the adequacy of the estimated models, uGMAR utilizes so-called quantile residuals and provides functions for graphical diagnostics as well as for calculating formal diagnostic tests. uGMAR also facilitates simulation from the processes and forecasting future values of the process by a simulation-based Monte Carlo method. I illustrate the use of uGMAR with the monthly U.S. interest rate spread between the 10-year and 1-year Treasury rates. In the third essay, I proceed to multivariate models and introduce a structural Gaussian mixture vector autoregressive model. The shocks are identified by combining simultaneous diagonalization of the reduced form error covariance matrices with constraints on the time-varying impact matrix. This leads to flexible identification conditions, and some the constraints are also testable. In an empirical application to quarterly U.S. data covering the period from 1953Q3 to 2021Q4, my model identifies two regimes: a stable inflation regime and an unstable inflation regime. The unstable inflation regime is characterized by high or volatile inflation, and it mainly prevails in the 1970's, early 1980's, during the Financial crisis, and in the COVID-19 crisis from 2020Q3 onwards. The stable inflation regime, in turn, is characterized by moderate inflation, and it prevails when the unstable inflation regime does not. While the effects of the monetary policy shock are relatively symmetric in the unstable inflation regime, I find strong asymmetries with respect to the sign and size of the shock as well as to the initial state of the economy in the stable inflation regime. On average, the real effects of the monetary policy shock are somewhat stronger in the stable inflation regime than in the unstable inflation regime. The last essay introduces a new mixture vector autoregressive model based on Gaussian and Student's t distributions. The model incorporates conditionally homoskedastic linear Gaussian vector autoregressions and conditionally heteroskedastic linear Student's t vector autoregressions as its mixture components. For a pth order model, the mixing weights depend on the full distribution of the preceding p observations. The specific formulation of the mixing weights leads to attractive practical and theoretical properties such as ergodicity and full knowledge of the stationary distribution of p+1 consecutive observations. The empirical application studies asymmetries in the effects of Euro area monetary policy shocks. My model identifies two regimes: a low-growth regime and a high-growth regime. The low-growth regime is characterized by negative (but volatile) output gap, and it mainly prevails after the Financial crisis. The high-growth regime is characterized by positive output gap, and it mainly dominates before the Financial crisis. I find the real effects less enduring for an expansionary than for a contractionary monetary policy shock. On average, the inflationary effects of the monetary policy shock are stronger in the high-growth regime than in the low-growth regime.Väitöskirja esittää uusia tilastollisia malleja perättäisinä ajanhetkinä mitattavien eri tilojen välillä vaihtelevien ilmiöiden tutkimiseen. Empiiriset sovellukset makrotalouteen ja finanssiaikasarjoihin havainnollistavat niiden hyödyllisyyttä. Lisäksi väitöskirjaan liittyy kaksi R-kielellä kirjoitettua avoimen lähdekoodin ohjelmistopakettia nimiltään uGMAR ja gmvarkit, jotka tarjoavat kattavan kokoelman työkaluja esitettyjen mallien estimointiin ja muuhun numeeriseen analyysiin

The geometry of nonlinear least squares with applications to sloppy models and optimization

Parameter estimation by nonlinear least squares minimization is a common problem with an elegant geometric interpretation: the possible parameter values of a model induce a manifold in the space of data predictions. The minimization problem is then to find the point on the manifold closest to the data. We show that the model manifolds of a large class of models, known as sloppy models, have many universal features; they are characterized by a geometric series of widths, extrinsic curvatures, and parameter-effects curvatures. A number of common difficulties in optimizing least squares problems are due to this common structure. First, algorithms tend to run into the boundaries of the model manifold, causing parameters to diverge or become unphysical. We introduce the model graph as an extension of the model manifold to remedy this problem. We argue that appropriate priors can remove the boundaries and improve convergence rates. We show that typical fits will have many evaporated parameters. Second, bare model parameters are usually ill-suited to describing model behavior; cost contours in parameter space tend to form hierarchies of plateaus and canyons. Geometrically, we understand this inconvenient parametrization as an extremely skewed coordinate basis and show that it induces a large parameter-effects curvature on the manifold. Using coordinates based on geodesic motion, these narrow canyons are transformed in many cases into a single quadratic, isotropic basin. We interpret the modified Gauss-Newton and Levenberg-Marquardt fitting algorithms as an Euler approximation to geodesic motion in these natural coordinates on the model manifold and the model graph respectively. By adding a geodesic acceleration adjustment to these algorithms, we alleviate the difficulties from parameter-effects curvature, improving both efficiency and success rates at finding good fits.Comment: 40 pages, 29 Figure

Change-point Problem and Regression: An Annotated Bibliography

The problems of identifying changes at unknown times and of estimating the location of changes in stochastic processes are referred to as the change-point problem or, in the Eastern literature, as disorder . The change-point problem, first introduced in the quality control context, has since developed into a fundamental problem in the areas of statistical control theory, stationarity of a stochastic process, estimation of the current position of a time series, testing and estimation of change in the patterns of a regression model, and most recently in the comparison and matching of DNA sequences in microarray data analysis. Numerous methodological approaches have been implemented in examining change-point models. Maximum-likelihood estimation, Bayesian estimation, isotonic regression, piecewise regression, quasi-likelihood and non-parametric regression are among the methods which have been applied to resolving challenges in change-point problems. Grid-searching approaches have also been used to examine the change-point problem. Statistical analysis of change-point problems depends on the method of data collection. If the data collection is ongoing until some random time, then the appropriate statistical procedure is called sequential. If, however, a large finite set of data is collected with the purpose of determining if at least one change-point occurred, then this may be referred to as non-sequential. Not surprisingly, both the former and the latter have a rich literature with much of the earlier work focusing on sequential methods inspired by applications in quality control for industrial processes. In the regression literature, the change-point model is also referred to as two- or multiple-phase regression, switching regression, segmented regression, two-stage least squares (Shaban, 1980), or broken-line regression. The area of the change-point problem has been the subject of intensive research in the past half-century. The subject has evolved considerably and found applications in many different areas. It seems rather impossible to summarize all of the research carried out over the past 50 years on the change-point problem. We have therefore confined ourselves to those articles on change-point problems which pertain to regression. The important branch of sequential procedures in change-point problems has been left out entirely. We refer the readers to the seminal review papers by Lai (1995, 2001). The so called structural change models, which occupy a considerable portion of the research in the area of change-point, particularly among econometricians, have not been fully considered. We refer the reader to Perron (2005) for an updated review in this area. Articles on change-point in time series are considered only if the methodologies presented in the paper pertain to regression analysis